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Even as the president has touted the growth of charter schools and his education secretary has decried state caps on their numbers, a new study from Stanford University has found that the nation’s charter schools have not significantly raised student achievement when compared with traditional public schools.

The study of collective reading and math progress in 2,403 charter schools in 15 states and cities, including the District of Columbia was released Monday by researchers at Stanford’s Center for Research on Education Outcomes (CREDO). It showed that almost half of the charter schools produced results similar to those from comparable public schools, and schools producing worse results than the traditional schools outnumbered those with better numbers by more than 2 to 1.

The study matched students in charter schools with “twins” of the same demographic and educational-success levels who were enrolled in traditional public schools. The study then compared the achievement on standardized tests of the two groups of students.

The study said 46 percent of charter schools posted results “statistically indistinguishable” from what the “twin” students in traditional schools achieved. Just 17 percent of charter schools outpaced traditional schools, while 37 percent of charter schools had academic results significantly below the performance of pupils in conventional schools.

The bright spot: Students who live in poverty and students who had limited use of English were found to do better academically in charter schools, with gains posted in reading and math, researchers said.

“Charter schools that are organized around a mission to teach the most economically disadvantaged students in particular seem to have developed expertise in serving these communities,” the study said in explanation.

Length of time in a charter school also seems to help, the researchers found. First-year students posted learning declines; but by the second and third year in charter schools, students on average made significant positive gains.

Blacks and Hispanics also did worse than their public school “twins,” the researchers said, noting the impact of family backgrounds on achievement. In contrast, students who aren’t poor or classified as English-language learners did “notably worse” in charter schools, the researchers found, adding that some students in charters may be “off mission.”

Lead study author Margaret Raymond, who spoke during a teleconference Monday, said wild variations in student achievement were reported from state to state and presented a serious quality challenge for the charter school community.

The CREDO researchers also called on states to replicate good charter school practices and models, while adding that those who seek to open new charter schools need to hold up their end of the charter bargain, “accountability for flexibility,” and be willing to close those schools that are not working.

“The good news is that we have a number of states where the average charter school performance is superior” to traditional public schools, Ms. Raymond said in releasing the findings.

Those states and cities with higher charter school gains in both math and reading include Arkansas, Denver, Chicago, Louisiana and Missouri. For six other states, however, the opposite was true, with students in Arizona, Florida, Minnesota, New Mexico, Ohio and Texas on average learning less than those in traditional school environments. Charter schools in California, Georgia, North Carolina and the District of Columbia did about as well as their traditional-school peers, the study found.

Michael Petrilli, vice president for national programs and policy at the Thomas B. Fordham Foundation in Washington, calls the study results disappointing but not surprising. He said the study, while credible, was not a “gold standard” and does not represent the last word on charter success.

“We know that in many parts of the country, the best schools are charter schools and in others, charter schools are the worst schools,” Mr. Petrilli said. “When you give people more freedom, good people can create fantastic charter schools. I think the charter school movement has to wrestle now with the low-performing schools among it. … We know with any start-up organization, some will fail.”

President Obama pledged during the campaign to double funding for charter schools, and Education Secretary Arne Duncan has decried caps on the number of charters that states will allow. The Stanford research found that in states that don’t have caps, charter schools outperform traditional public schools, while states with caps tend to do worse.

Forty states, along with the District and Puerto Rico, have authorized about 4,600 charter schools, serving an estimated 1.4 million children. Under the Obama stimulus plan, about $650 million is available to states under the education department’s discretionary Innovation Fund, with an additional $211 million directed at charter-specific programs, according to the National Alliance for Public Charter Schools.

The Stanford study was criticized by a charter proponent, the Center for Education Reform in Washington, which disputed the research methodology and said the analysis did not fully address differences in state charter laws.

“The CREDO report fails the most important and most objective test of student data analysis through their use of virtual twins to replicate real student growth by creating ‘straw men’ subjects,” CER President Jeanne Allen said. “This suggests that virtual methodology can overcome comparative analysis by making the study world look real, act real and sound real.”

The center questioned the CREDO findings that said students in poverty showed gains, while black and Hispanic students were found to be lower-performing, despite the higher rates of poverty in those groups.

“Well-documented and nationally recognized survey work representing more than a third of all charters finds such demographics to be one and the same,” the CER said.